Question: Which of the following numbers is a factor of 154? ${4,6,9,10,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $154$ by each of our answer choices. $154 \div 4 = 38\text{ R }2$ $154 \div 6 = 25\text{ R }4$ $154 \div 9 = 17\text{ R }1$ $154 \div 10 = 15\text{ R }4$ $154 \div 14 = 11$ The only answer choice that divides into $154$ with no remainder is $14$ $ 11$ $14$ $154$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $154$ $154 = 2\times7\times11 14 = 2\times7$ Therefore the only factor of $154$ out of our choices is $14$. We can say that $154$ is divisible by $14$.